: why is she appearing to hide the fact that it's due to her and Master
: Chief's actions?

This is similar to what Red Loser posted above, but anyway...

Imagine that you're Foehammer. A call comes in from a very dangerous zone... "Hey, can you pick us up? We just set off the Autumn's core so we could blow it up, and we'd like to get out of here."

I think my first reaction would be to avoid letting a very clearly psychotic cyborg and AI board my ship. ;-) Sure, Cortana and the Chief could have taken the time to explain, but they're on a tight schedule. Phrasing it like an accident means that Foehammer won't waste time asking them what they've been drinking and will get straight to the pickup job. It all really comes down to whether or not Cortana planned to explain her little white lie after getting picked up.

: For that matter, why have none of the other human forces been ordered to
: abandon Halo by any means? Doing so is hardly going to alert the Covenant,
: since they have already been ordered off Halo themselves and would see
: nothing odd in the humans leaving too.

Who says they haven't? Either Cortana has been unable to pick up an evac signal, and/or the vast majority of human soldiers have already been Flooded. Remember, the Covenant at least have energy shields to delay their infection... the humans are much more vulnerable, even with their shotguns.

: As an aside, but connected with this, is the issue of getting off Halo. At
: first, after initially setting the PoA's engines to detonate, Cortana
: says: "That should give us enough time to make it to a lifeboat and
: put some distance between ourselves and Halo before the detonation."

: One, why would they be any lifeboats left? Two, I would have thought it
: doubtful that any that were left would still be operable by now. Three,
: would a lifeboat actually be capable of getting them back to Earth or any
: other human outpost? Possibly. Four, and most importantly, it implies that
: originally Cortana had no intention of contacting Foe Hammer and thus
: reinforces the suspicion that she was/is not interested in the survival of
: any other UNSC forces.

Apparently, a lifeboat did remain, and would have been sufficient. If you look at the storyboards on the official site, the original plan was for the final Warthog run to end at a lifeboat bay and have the Chief climb on board, blast one last Flood, and take off. No Longsword involved.